Multiresolution Mode Decomposition for Adaptive Time Series Analysis

Yang, Haizhao

doi:10.48550/arxiv.1709.06880

Cited by 4 publications

(22 citation statements)

References 28 publications

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“…We only consider disjoint sets {Ω k } k in this paper. In more complicated cases when there are overlapping grains, it would be interesting to extend the mode decomposition techniques for one-dimensional oscillatory signals in [31,33] to two-dimensional so as to decompose overlapping grains. Hence, not considering grain boundaries, the polycrystal image f : Ω → R can be modeled as (1) f…”

Section: Crystal Image Modeling and Synchrosqueezed Transform (Sst)mentioning

confidence: 99%

Phase-Space Sketching for Crystal Image Analysis Based on Synchrosqueezed Transforms

Lu¹,

Yang²

2018

SIAM J. Imaging Sci.

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Recent developments of imaging techniques enable researchers to visualize materials at the atomic resolution to better understand the microscopic structures of materials. This paper aims at automatic and quantitative characterization of potentially complicated microscopic crystal images, providing feedback to tweak theories and improve synthesis in materials science. As such, an efficient phase-space sketching method is proposed to encode microscopic crystal images in a translation, rotation, illumination, and scale invariant representation, which is also stable with respect to small deformations. Based on the phase-space sketching, we generalize our previous analysis framework for crystal images with simple structures to those with complicated geometry.

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Section: Crystal Image Modeling and Synchrosqueezed Transform (Sst)mentioning

confidence: 99%

Phase-Space Sketching for Crystal Image Analysis Based on Synchrosqueezed Transforms

Lu¹,

Yang²

2018

SIAM J. Imaging Sci.

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“…From the computational point of veiw, RDSA takes only O(mL log L) operations to solve the MMD problem by taking advantage of the NUFFT, where L is the length of the signal and m is the number of iterations. As we shall see later, the speedup of RDSA over RDBR in [34] can be as large as 1000. From the theoretical point of view, RDSA builds the bridge between FFT-based analysis and the RDBR, leading to a complete convergence analysis and filling the gap of theoretical analysis of FFT-based approaches in [26,27].…”

Section: Introductionmentioning

confidence: 99%

“…To better analyze time series with time-dependent amplitudes, phases, and shapes, the multiresolution mode decomposition (MMD) is proposed in [34] of the form…”

Section: Introductionmentioning

confidence: 99%

“…It was shown in [34] that the MIMF model can capture the evolution variance, which is more important than the average evolution patterns of oscillatory data, for detecting diseases and measuring health risk. Let M be the operator for computing the -banded multiresolution approximation to a MIMF f (t), i.e.,…”

Section: Introductionmentioning

confidence: 99%

“…Applying the idea of recursive diffeomorphism-based regression (RDBR) [28], [34] has proposed a recursive scheme for decomposing f (t) into several MIMF's, {f k (t)}. Due to the repeated application of the expensive diffeomorphism-based regression, the method in [34] is not suitable for analyzing large data sets, especially when real-time analysis is required. Analyzing a single record of a high-resolution ECG or PPG signal with a few minutes of duration could take a whole day.…”

Section: Introductionmentioning

confidence: 99%

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A Fast Algorithm for Multiresolution Mode Decomposition

Tang¹,

Yang²

2017

Preprint

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Multiresolution mode decomposition (MMD) is an adaptive tool to analyze a time serieswith time-dependent amplitudes, frequencies, and waveforms. The multiresolution expansion coefficients {a n,k }, {b n,k }, and the shape function series {s cn,k (t)} and {s sn,k (t)} provide innovative features for adaptive time series analysis. The MMD aims at identifying these MIMF's (including their multiresolution expansion coefficients and shape functions series) from their superposition. However, due to the lack of efficient algorithms to solve the MMD problem, the application of MMD for large-scale data science is prohibitive, especially for real-time data analysis. This paper proposes a fast algorithm for solving the MMD problem based on recursive diffeomorphism-based spectral analysis (RDSA). RDSA admits highly efficient numerical implementation via the nonuniform fast Fourier transform (NUFFT); its convergence and accuracy can be guaranteed theoretically. Numerical examples from synthetic data and natural phenomena are given to demonstrate the efficiency of the proposed method.

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Phase Space Sketching for Crystal Image Analysis based on Synchrosqueezed Transforms

Lu¹,

Yang²

2017

Preprint

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Multiresolution Mode Decomposition for Adaptive Time Series Analysis

Cited by 4 publications

References 28 publications

Phase-Space Sketching for Crystal Image Analysis Based on Synchrosqueezed Transforms

Phase-Space Sketching for Crystal Image Analysis Based on Synchrosqueezed Transforms

A Fast Algorithm for Multiresolution Mode Decomposition

Phase Space Sketching for Crystal Image Analysis based on Synchrosqueezed Transforms

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